Modeling population dynamics that include mutualistic interactions is an important and complex
problem in theoretical biology and quantitative ecology. Mutualistic interactions, which are
generally considered relationships in which two or more species benefit from each other’s
presence, play a significant role in determining population dyanmics, and are essential to fully
understanding the dynamics of interacting species. However, mutualistic interactions are a
historically understudied topic in ecology; accurately describing populations in multi-species
interactions is inherently challenging (Hastings & Powell, 1991), and models describing these
populations increase greatly in complexity as the intricacy and interdependence of the relationship
increases. As such, there have been relatively few attempts within the field to fully account for the
particulars of these relationships. Through numerical simulation of lycaenid butterfly and aphid
populations together with deterministic and stochastic mathematical models, this research aims to
more thoroughly explore the facets of mutualistic and competitive interactions in population
dynamics. By refining a previous model for lycaenid butterfly populations (Forister, Gompert,
Nice, & Fordyce, 2010) and by adapting the models to include the dynamics of two interactive
species, ants and aphids, we hope to generate a model which simultaneously predicts the
fluctuation in the focal species while providing insight to the rich and complex interplay of
mutualistic and competitive interactions in theoretical ecology. By using this model to examine the
population dynamics of these species, we hope to generate a method which will be useful in
explaining endangered lycaenid butterfly populations as well as understanding the role of
mutualism in the context of quantitative and theoretical ecology
